# Is the difference distribution table of AES S-box uniform?

I am studying about various block ciphers and their weaknesses, so I have a doubt about AES S-boxes, Is the difference distribution table of AES uniform ?

• I meant difference distribution table of S-box of AES, like in DES the DDT of S-boxes are not uniform Commented Jul 11, 2016 at 17:31
• @TruthSerum A difference distribution table is what they call the table that contains sbox input difference/output difference/propagation probabilities. Commented Jul 11, 2016 at 17:40
• Its a matrix with all possible input differentials as rows and corresponding output differentials as columns..As said by @Ella Rose it provides the probability of an output differential to specific input differencial. :) Commented Jul 11, 2016 at 17:44

The difference distribution table for the AES s-box contains mostly probability 2/256 differentials. However, there is a single probability 4/256 for each input/output difference. I uploaded a dump of the table here so that you can see.

The code used to produce this table can be found here. Disclaimer: This is my personal github.

If by "uniform", you mean all values equal, the case is no. If you meant "differential uniformity", that is a term with a precise meaning:

From this paper, they define differential uniformity as "A mapping is called differentially uniform if for every non-zero input difference and any output difference the number of possible inputs has a uniform upper bound".

The AES s-box is a differential 4 uniform function

• Thanks a lot @Ella Rose for your reply, i actually expected the DDT to be something like this,its the DDT of S1 box of DES ...as we see it is not that uniform i.e. not every column (output diffrencial) has equal value(probability) for a particular row(input differencial) Commented Jul 11, 2016 at 18:03
• well i see it has mostly 2/256 and one 4/256 in every row..can you please share the code to get that table ? and can i say AES Sbox DDT is more uniform than DES S-boxes DDT @Ella Rose ...Thank you in advance Commented Jul 11, 2016 at 18:16
• @Abhinavsingh, Funfact: if you have too many ultra-low probability differentials, an impossible-differential-attack may apply, like it did to SKIPJACK (didn't break it completely though). Commented Jul 11, 2016 at 18:32
• @SEJPM thank you for your reply, I know about impossible differential cryptanalysis and it's been successfully applied on 7 rounds of AES. What i wanted to be sure of is AES Sbox DDT more uniform than DES S-boxes DDT ? and can we say AES Sbox is more secure towards differential cryptanalysis? Commented Jul 11, 2016 at 18:54

AES S-box DDT is not uniform but it has a higher resistant to differential attacks than DES because of maximum probablity of input output pair of differential is 4/256.